Neural Estimation and Optimization of Directed Information over Continuous Spaces

TL;DR

This paper introduces a neural network-based method for estimating and optimizing directed information between continuous stochastic processes, applicable to channels with memory, with proven consistency and empirical validation.

Contribution

It presents a novel RNN-based estimator and optimizer for directed information that does not require prior distribution knowledge and is scalable to continuous processes.

Findings

Estimator is consistent and scalable.

Method accurately estimates channel capacity.

Optimized input generator learns meaningful mappings.

Abstract

This work develops a new method for estimating and optimizing the directed information rate between two jointly stationary and ergodic stochastic processes. Building upon recent advances in machine learning, we propose a recurrent neural network (RNN)-based estimator which is optimized via gradient ascent over the RNN parameters. The estimator does not require prior knowledge of the underlying joint and marginal distributions. The estimator is also readily optimized over continuous input processes realized by a deep generative model. We prove consistency of the proposed estimation and optimization methods and combine them to obtain end-to-end performance guarantees. Applications for channel capacity estimation of continuous channels with memory are explored, and empirical results demonstrating the scalability and accuracy of our method are provided. When the channel is memoryless, we investigate the mapping learned by the optimized input generator.